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Search: id:A082639
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| A082639 |
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Numbers n such that 2*n*(n+2) is a square. |
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+0
5
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| 0, 2, 16, 98, 576, 3362, 19600, 114242, 665856, 3880898, 22619536, 131836322, 768398400, 4478554082, 26102926096, 152139002498, 886731088896, 5168247530882, 30122754096400, 175568277047522, 1023286908188736
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OFFSET
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1,2
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COMMENT
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Even indexed terms are squares. Their square roots form the sequence A005319. Odd indexed terms divided by 2 are squares. Their square roots form the sequence A002315. (index starts at 0)
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FORMULA
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a(n)=(1/2)*(s^n+t^n)-1, where s=3+2*sqrt(2), t=3-2*sqrt(2). Note: s=1/t. a(n)=6*a(n-1)-a(n-2)+4, a(0)=0, a(1)=2.
a(n) = 1/kappa(sqrt(2)/A001542(n)); a(n) = 1/kappa(sqrt(8)/A005319(n)) where kappa(x) is the sum of successive remainders by computing the euclidean algorithm for (1, x). - Thomas Baruchel (baruchel(AT)users.sourceforge.net), Nov 29 2003
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MATHEMATICA
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a[0] = 0; a[1] = 2; a[n_] := a[n] = 6a[n - 1] - a[n - 2] + 4; Table[ a[n], {n, 0, 20}]
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CROSSREFS
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Cf. A005319, A002315.
A001541(n) - 1.
Adjacent sequences: A082636 A082637 A082638 this_sequence A082640 A082641 A082642
Sequence in context: A038749 A002699 A005058 this_sequence A043016 A032260 A059204
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KEYWORD
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easy,nonn
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AUTHOR
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Jim Buddenhagen (jbuddenh(AT)gmail.com), May 15 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 15 2003
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